Tangrams and Fractions

  Being the only high school math teacher, the secretaries put all the catalogues with math things in my box.  Usually I throw them away without looking in them but the other day, I decided to check out the books just because I'm looking for new ideas.

I came across a book on using Tangrams to teach fractions.  That sparked my curiosity because I've used them to teach geometry concepts of convex and concave but never for fractions.

One way to use Tangrams to teach fractions is to have students make their own out of the stiffer construction paper.  Students use a 6 by 6 inch piece to create the set.  They start by folding the paper in half from corner to corner and then cut along the line so they now have two triangles.  Take one triangle and fold it again in half to make two smaller trangles so you have two like the tan and light blue ones.

The student then takes the point of the other triangle and fold it to the midpoint of the longest side.  Cut off the triangular piece at the top so you are left with an isosceles trapezoid.  This triangle is the green one. Fold it in half so you have a right trapezoid shape before unfolding.  Then take the corner on the longer side and fold it to the middle on the longer side before unfolding it.  Then fold the opposite short corner on the other side of the middle fold to the midpoint opposite.  Then unfold it.  You should see two smaller triangles such as the darker blue and yellow ones on each side of a square and the parallelogram.  Cut the shapes and there are the seven pieces of the Tangram.

Each of the two large triangles represent one fourth of the total shape.  The parallelogram, square and mid-sized triangle represent one eight each of the total shape.  The two smallest triangles each represent one sixteenth of the square.  If these directions do not make sense, check out this site with the directions and worksheets.


If you check out page one of this pdf, you'll see it assigns values of one to various shapes in the Tangram so students are looking at fractions greater than one.  In addition, this pdf has students taking their learning and applying it to several nontraditional Tangrams to determine the fraction of each shape.  It makes a nice extension activity requiring transference of knowledge.

If you wonder why I'm addressing the topic of fractions in a blog that looks at topics for middle school and high school, I have students who arrive in 9th grade who do not have a firm foundation in fractions and struggle.  The above topic gives them a different perspective to fractions and might be the one item they need to help them understand the topic.

If you need to you can extend this topic by having students change the fractions into decimals and percents if you need to work on showing the relationship between the three.

Let me know what you think, I'd love to hear. Have a great day.